{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Student Admissions with Neural Networks in Keras\n",
    "In this notebook, we predict student admissions to graduate school at UCLA based on three pieces of data:\n",
    "- GRE Scores (Test)\n",
    "- GPA Scores (Grades)\n",
    "- Class rank (1-4)\n",
    "\n",
    "The dataset originally came from here: http://www.ats.ucla.edu/\n",
    "\n",
    "## Loading the data\n",
    "To load the data and format it nicely, we will use two very useful packages called Pandas and Numpy. You can read on the documentation here:\n",
    "- https://pandas.pydata.org/pandas-docs/stable/\n",
    "- https://docs.scipy.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>admit</th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>rank</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>380</td>\n",
       "      <td>3.61</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>660</td>\n",
       "      <td>3.67</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>800</td>\n",
       "      <td>4.00</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>640</td>\n",
       "      <td>3.19</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>520</td>\n",
       "      <td>2.93</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>760</td>\n",
       "      <td>3.00</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>560</td>\n",
       "      <td>2.98</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>400</td>\n",
       "      <td>3.08</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>540</td>\n",
       "      <td>3.39</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>700</td>\n",
       "      <td>3.92</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   admit  gre   gpa  rank\n",
       "0      0  380  3.61     3\n",
       "1      1  660  3.67     3\n",
       "2      1  800  4.00     1\n",
       "3      1  640  3.19     4\n",
       "4      0  520  2.93     4\n",
       "5      1  760  3.00     2\n",
       "6      1  560  2.98     1\n",
       "7      0  400  3.08     2\n",
       "8      1  540  3.39     3\n",
       "9      0  700  3.92     2"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Importing pandas and numpy\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Reading the csv file into a pandas DataFrame\n",
    "data = pd.read_csv('student_data.csv')\n",
    "\n",
    "# Printing out the first 10 rows of our data\n",
    "data[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the data\n",
    "\n",
    "First let's make a plot of our data to see how it looks. In order to have a 2D plot, let's ingore the rank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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K9MO1NaD0HF4TZNoYNwLDT5VUB1AmItcAs4AblVLzE1Y3d4nILBGZBfwb8HjM22ej74nI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\nMzOr4oBhZmZVHDDMzKzKLyUWiZ65DNiaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e46db8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Importing matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# Function to help us plot\n",
    "def plot_points(data):\n",
    "    X = np.array(data[[\"gre\",\"gpa\"]])\n",
    "    y = np.array(data[\"admit\"])\n",
    "    admitted = X[np.argwhere(y==1)]\n",
    "    rejected = X[np.argwhere(y==0)]\n",
    "    plt.scatter([s[0][0] for s in rejected], [s[0][1] for s in rejected], s = 25, color = 'red', edgecolor = 'k')\n",
    "    plt.scatter([s[0][0] for s in admitted], [s[0][1] for s in admitted], s = 25, color = 'cyan', edgecolor = 'k')\n",
    "    plt.xlabel('Test (GRE)')\n",
    "    plt.ylabel('Grades (GPA)')\n",
    "    \n",
    "# Plotting the points\n",
    "plot_points(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Roughly, it looks like the students with high scores in the grades and test passed, while the ones with low scores didn't, but the data is not as nicely separable as we hoped it would. Maybe it would help to take the rank into account? Let's make 4 plots, each one for each rank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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13BfAHb3M6k+lO6+dy+NzJ9wWEV+fY/rKVk5Q8E2qetzRy6w+lRoUSu2n8HWg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\nYGZmRQ4KZmZW9P8BxtTlTs7j/8sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e46db470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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w5jW4Ml0yWVD/b5mM1qfweWD9kNs1wGqctBVrgKUB1cuYMfEaBMO03GckEuHY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\nmEEWFIwxxgz6f9pMDvq3yWqAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e1819cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sAl4BfFZVP1Bk3c8AT6jqhyZ47grgCoBFixYt+/Wvf+25zMaUm9+9dSxPkfGD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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e17c1da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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esny5Mzoa/aOPjnpLPp+Z+KtlbGzMu7u7fdOmTd7d3e1jY2O1DikTiKZqivUZ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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e17a5240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Separating the ranks\n",
    "data_rank1 = data[data[\"rank\"]==1]\n",
    "data_rank2 = data[data[\"rank\"]==2]\n",
    "data_rank3 = data[data[\"rank\"]==3]\n",
    "data_rank4 = data[data[\"rank\"]==4]\n",
    "\n",
    "# Plotting the graphs\n",
    "plot_points(data_rank1)\n",
    "plt.title(\"Rank 1\")\n",
    "plt.show()\n",
    "plot_points(data_rank2)\n",
    "plt.title(\"Rank 2\")\n",
    "plt.show()\n",
    "plot_points(data_rank3)\n",
    "plt.title(\"Rank 3\")\n",
    "plt.show()\n",
    "plot_points(data_rank4)\n",
    "plt.title(\"Rank 4\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks more promising, as it seems that the lower the rank, the higher the acceptance rate. Let's use the rank as one of our inputs. In order to do this, we should one-hot encode it.\n",
    "\n",
    "## One-hot encoding the rank\n",
    "For this, we'll use the `get_dummies` function in pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>admit</th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>rank_1</th>\n",
       "      <th>rank_2</th>\n",
       "      <th>rank_3</th>\n",
       "      <th>rank_4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>380</td>\n",
       "      <td>3.61</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>660</td>\n",
       "      <td>3.67</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>800</td>\n",
       "      <td>4.00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>640</td>\n",
       "      <td>3.19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>520</td>\n",
       "      <td>2.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>760</td>\n",
       "      <td>3.00</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>560</td>\n",
       "      <td>2.98</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>400</td>\n",
       "      <td>3.08</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>540</td>\n",
       "      <td>3.39</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>700</td>\n",
       "      <td>3.92</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   admit  gre   gpa  rank_1  rank_2  rank_3  rank_4\n",
       "0      0  380  3.61       0       0       1       0\n",
       "1      1  660  3.67       0       0       1       0\n",
       "2      1  800  4.00       1       0       0       0\n",
       "3      1  640  3.19       0       0       0       1\n",
       "4      0  520  2.93       0       0       0       1\n",
       "5      1  760  3.00       0       1       0       0\n",
       "6      1  560  2.98       1       0       0       0\n",
       "7      0  400  3.08       0       1       0       0\n",
       "8      1  540  3.39       0       0       1       0\n",
       "9      0  700  3.92       0       1       0       0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make dummy variables for rank\n",
    "one_hot_data = pd.concat([data, pd.get_dummies(data['rank'], prefix='rank')], axis=1)\n",
    "\n",
    "# Drop the previous rank column\n",
    "one_hot_data = one_hot_data.drop('rank', axis=1)\n",
    "\n",
    "# Print the first 10 rows of our data\n",
    "one_hot_data[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling the data\n",
    "The next step is to scale the data. We notice that the range for grades is 1.0-4.0, whereas the range for test scores is roughly 200-800, which is much larger. This means our data is skewed, and that makes it hard for a neural network to handle. Let's fit our two features into a range of 0-1, by dividing the grades by 4.0, and the test score by 800."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>admit</th>\n",
       "      <th>gre</th>\n",
       "      <th>gpa</th>\n",
       "      <th>rank_1</th>\n",
       "      <th>rank_2</th>\n",
       "      <th>rank_3</th>\n",
       "      <th>rank_4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.475</td>\n",
       "      <td>0.9025</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.825</td>\n",
       "      <td>0.9175</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0.800</td>\n",
       "      <td>0.7975</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0.650</td>\n",
       "      <td>0.7325</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>0.950</td>\n",
       "      <td>0.7500</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>0.700</td>\n",
       "      <td>0.7450</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.7700</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>0.675</td>\n",
       "      <td>0.8475</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0.875</td>\n",
       "      <td>0.9800</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   admit    gre     gpa  rank_1  rank_2  rank_3  rank_4\n",
       "0      0  0.475  0.9025       0       0       1       0\n",
       "1      1  0.825  0.9175       0       0       1       0\n",
       "2      1  1.000  1.0000       1       0       0       0\n",
       "3      1  0.800  0.7975       0       0       0       1\n",
       "4      0  0.650  0.7325       0       0       0       1\n",
       "5      1  0.950  0.7500       0       1       0       0\n",
       "6      1  0.700  0.7450       1       0       0       0\n",
       "7      0  0.500  0.7700       0       1       0       0\n",
       "8      1  0.675  0.8475       0       0       1       0\n",
       "9      0  0.875  0.9800       0       1       0       0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Copying our data\n",
    "processed_data = one_hot_data[:]\n",
    "\n",
    "# Scaling the columns\n",
    "processed_data['gre'] = processed_data['gre']/800\n",
    "processed_data['gpa'] = processed_data['gpa']/4.0\n",
    "processed_data[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting the data into Training and Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to test our algorithm, we'll split the data into a Training and a Testing set. The size of the testing set will be 10% of the total data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training samples is 360\n",
      "Number of testing samples is 40\n",
      "     admit    gre     gpa  rank_1  rank_2  rank_3  rank_4\n",
      "81       0  0.775  0.7675       0       1       0       0\n",
      "110      0  0.850  0.7700       0       0       0       1\n",
      "156      0  0.700  0.6300       0       1       0       0\n",
      "261      0  0.550  0.7875       0       1       0       0\n",
      "12       1  0.950  1.0000       1       0       0       0\n",
      "391      1  0.825  0.9700       0       1       0       0\n",
      "169      0  0.750  0.9050       0       0       1       0\n",
      "3        1  0.800  0.7975       0       0       0       1\n",
      "101      0  0.725  0.8925       0       0       1       0\n",
      "35       0  0.500  0.7625       0       1       0       0\n",
      "    admit    gre     gpa  rank_1  rank_2  rank_3  rank_4\n",
      "6       1  0.700  0.7450       1       0       0       0\n",
      "9       0  0.875  0.9800       0       1       0       0\n",
      "38      1  0.625  0.7825       0       1       0       0\n",
      "44      0  0.875  0.7350       0       1       0       0\n",
      "46      1  0.725  0.8650       0       1       0       0\n",
      "50      0  0.800  0.9650       0       0       1       0\n",
      "64      0  0.725  1.0000       0       0       1       0\n",
      "67      0  0.775  0.8250       1       0       0       0\n",
      "68      0  0.725  0.9225       1       0       0       0\n",
      "69      0  1.000  0.9325       1       0       0       0\n"
     ]
    }
   ],
   "source": [
    "sample = np.random.choice(processed_data.index, size=int(len(processed_data)*0.9), replace=False)\n",
    "train_data, test_data = processed_data.iloc[sample], processed_data.drop(sample)\n",
    "\n",
    "print(\"Number of training samples is\", len(train_data))\n",
    "print(\"Number of testing samples is\", len(test_data))\n",
    "print(train_data[:10])\n",
    "print(test_data[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting the data into features and targets (labels)\n",
    "Now, as a final step before the training, we'll split the data into features (X) and targets (y).\n",
    "\n",
    "Also, in Keras, we need to one-hot encode the output. We'll do this with the `to_categorical function`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.775   0.7675  0.      1.      0.      0.    ]\n",
      " [ 0.85    0.77    0.      0.      0.      1.    ]\n",
      " [ 0.7     0.63    0.      1.      0.      0.    ]\n",
      " [ 0.55    0.7875  0.      1.      0.      0.    ]\n",
      " [ 0.95    1.      1.      0.      0.      0.    ]\n",
      " [ 0.825   0.97    0.      1.      0.      0.    ]\n",
      " [ 0.75    0.905   0.      0.      1.      0.    ]\n",
      " [ 0.8     0.7975  0.      0.      0.      1.    ]\n",
      " [ 0.725   0.8925  0.      0.      1.      0.    ]\n",
      " [ 0.5     0.7625  0.      1.      0.      0.    ]]\n",
      "[[ 1.  0.]\n",
      " [ 1.  0.]\n",
      " [ 1.  0.]\n",
      " [ 1.  0.]\n",
      " [ 0.  1.]\n",
      " [ 0.  1.]\n",
      " [ 1.  0.]\n",
      " [ 0.  1.]\n",
      " [ 1.  0.]\n",
      " [ 1.  0.]]\n"
     ]
    }
   ],
   "source": [
    "import keras\n",
    "\n",
    "# Separate data and one-hot encode the output\n",
    "# Note: We're also turning the data into numpy arrays, in order to train the model in Keras\n",
    "features = np.array(train_data.drop('admit', axis=1))\n",
    "targets = np.array(keras.utils.to_categorical(train_data['admit'], 2))\n",
    "features_test = np.array(test_data.drop('admit', axis=1))\n",
    "targets_test = np.array(keras.utils.to_categorical(test_data['admit'], 2))\n",
    "\n",
    "print(features[:10])\n",
    "print(targets[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the model architecture\n",
    "Here's where we use Keras to build our neural network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_1 (Dense)              (None, 128)               896       \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 64)                8256      \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 64)                0         \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 2)                 130       \n",
      "=================================================================\n",
      "Total params: 9,282\n",
      "Trainable params: 9,282\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Dropout, Activation\n",
    "from keras.optimizers import SGD\n",
    "from keras.utils import np_utils\n",
    "\n",
    "# Building the model\n",
    "model = Sequential()\n",
    "model.add(Dense(128, activation='relu', input_shape=(6,)))\n",
    "model.add(Dropout(.2))\n",
    "model.add(Dense(64, activation='relu'))\n",
    "model.add(Dropout(.1))\n",
    "model.add(Dense(2, activation='softmax'))\n",
    "\n",
    "# Compiling the model\n",
    "model.compile(loss = 'categorical_crossentropy', optimizer='adam', metrics=['accuracy'])\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f10c79d25c0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Training the model\n",
    "model.fit(features, targets, epochs=200, batch_size=100, verbose=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scoring the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 32/360 [=>............................] - ETA: 0s\n",
      " Training Accuracy: 0.722222222222\n",
      "32/40 [=======================>......] - ETA: 0s\n",
      " Testing Accuracy: 0.575\n"
     ]
    }
   ],
   "source": [
    "# Evaluating the model on the training and testing set\n",
    "score = model.evaluate(features, targets)\n",
    "print(\"\\n Training Accuracy:\", score[1])\n",
    "score = model.evaluate(features_test, targets_test)\n",
    "print(\"\\n Testing Accuracy:\", score[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Challenge: Play with the parameters!\n",
    "You can see that we made several decisions in our training. For instance, the number of layers, the sizes of the layers, the number of epochs, etc.\n",
    "It's your turn to play with parameters! Can you improve the accuracy? The following are other suggestions for these parameters. We'll learn the definitions later in the class:\n",
    "- Activation function: relu and sigmoid\n",
    "- Loss function: categorical_crossentropy, mean_squared_error\n",
    "- Optimizer: rmsprop, adam, ada"
   ]
  },
  {
   "cell_type": "code",
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